A model was developed in order to calculate the texture evolution of a growing film with large atomic diffusion on the surface. The tendency for lowest surface energy was taken as the driving force for the evolution. The orientation dependent surface energy gamma was approximated by a function with a sharp minimum in two crystallographic directions. The texture evolution was calculated, starting from various initial situations. With realistic assumptions it was found that a texture without preferential orientations evolved to a bimodal texture, and finally to a situation with only lowest gamma planes parallel to the substrate. For some initial situations a texture turn over from over crystallographic direction to another one can be expected. In all cases a sharpening of the angular distribution of the texture is found near the directions of a local minimum for gamma. For sufficiently large times the mean top diameter of the columns always increases with layer thickness. The calculated effects describe well a number of experimentally observed phenomena.